Translate into a number sentence7. Four less than seven is greater than zero

When we are adding/subtracting polynomials, we add or subtract like terms.

For example,

x^2 added with x^2 terms

x^4 added with x^4 terms

numbers (constants) added with numbers etc.

Since we are "adding" the 2nd parenthesis polynomial, we can take out the parenthesis and put them in order and them simply add/subtract(!) The steps are shown below:

Note: there were like terms with "x's" and "constants". We added/subtracted them only.

Given:

Given that a right triangles.

Required:

To find the value of variables in each triangle.

Explanation:

In right triangles,

(C)

Here,

Given the word problem, we can deduce the following information.

1. Two planes, which are 2320 miles apart, fly toward each other.

2. Their speeds differ by 80 mph.

3. They pass each other in 4 hours.

To find the speed of each plane, we use the formula:

distance = (rate)(time)

Since they are flying towards each other, the sum of both speeds is 2x+80. So,

distance = (rate)(time)

2320 miles = (2x+80 mph)(4 hrs)

Thus, the equation to solve this is:

2320 = (2x+80)(4)

Let's begin by listing out the information given to us:

Line AB is parallel to Line CD; this implies that the angle formed by the two lines are right angles (90 degrees)

E is the intersecting point of both lines AB & CD (figure attached)

Let us put this into its mathematical form:

Given:

A line passes through the point,

The slope of the line is m = -1.

The objective is to find the equation of the line in point-slope and slope-intercept form.

Explanation:

To find equation in point-slope form:

The general formula of point-slope form is,

On plugging the given values in equation (1),

To find the equation in slope-intercept form,

The general formula of slope-intercept form is,

On further solving the equation (2),

Hence,

The equation of the line in point-slope form is y+6 = -x+5.

The equation of the line in slope-intercept form is y = -x-1.

Answer:

x < 2 or x > -11

Step-by-step explanation:

b. 1. add 12 to both sides to get -1/3x > 33

2. multiply by -3/1 to both sides to get x > -11

a. 1) subtract 10 to both sides

2) divide by -6 to both sides

(h,k) are the coordinates of the vertex.

Use the given point (x,y) and the vertex (h,k) in the equation above to find the value of a:

Point: (-3 ,1) x = -3 y=1

Vertex: (-4 , -2) h= -4 k=-2

Use the vertex and a to write the equation:

ok

I'll use the law of gases to solve this problem

V1 = 42 cm^3

T1 = 84 °K

P = 8 Kg/cm^2

T2 = x

V2 = 74 cm^3

P2 = 10 kg/cm^2

Equation

P1V1/T1 = P2V2/T2

Solve for T2

T2 = P2V2T1 / P1V1

Substitution

T2 = (10*74*84) / (8*42)

Simplification

T2 = 62160 / 336

Result

T2 = 185°K

step 1

Find out the slope of the given line

we have

-(4/3)x+2y=4/3

isolate the variable y

2y=(4/3)x+(4/3)

Divide both sides by 2

y=(4/6)x+(4/6)

simplify

y=(2/3)x+(2/3)

the slope is m=2/3

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

that means

the slope of the perpendicular line to the given line is

m=-3/2

step 2

Find out the equation in slope-intercept form of the perpendicular line

y=mx+b

we have

m=-3/2

point ( 1,0)

substitute and solve for b

0=-(3/2)(1)+b

0=-(3/2)+b

b=3/2

therefore

the equation is

The budget is 20000 times greater.

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

Company A = $2 × [tex]10^{4}[/tex]e

Company B = $ 5 × [tex]10^{8}[/tex]

The difference = $2 × [tex]10^{4}[/tex]

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Given the table showing the number of days since wound began to heal and area of wound in square millimeters

To determine the statement that are correct from the option provided

From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of

Suppose that an expression to represent the area of wound is

The modelled expression from the table is

Let us use the modelled expression to verify each of the given conditions

The modelled expression can be simplified as shown below:

Then, we have the modelled expression becomes

From the two modelled expression we can see that

Then we can conclude that the two conditions that are true from the options are

If the value of c = n, the value of a is 31.25, and

If the value of c = n, the value of b is 0.8

Answer

The rate of change of both functions is 2.

Explanation

To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.

Rate of change of function A

Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 16 - 14 = 2

Δx = (x₂ - x₁) = 8 - 7 = 1

⇒ Rate of change = 2/1 = 2

Rate of change of function B

From the graph

Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 6 - 4 = 2

Δx = (x₂ - x₁) = 3 - 2 = 1

⇒ Rate of change = 2/1 = 2

Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"

The value of k when one angle measures 140°, and another angle measures (5k + 85)° and if the angles are vertical angles is 11.

Vertical angles are angles opposite each other where two lines cross.

Note: Vertical angles are equal.

To calculate the value of k, we use the principle of vertical angle

From the question,

Solve for k

Divide both side by the coefficient of k (5)

Hence, the value of k is 11.

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There are two known angles in such a manner:

We know that the sum of internal angles of a triangle is equal to 180 degrees. This means that we can find the missing angle by adding all the internal angles and making it equal to 180

The missing angle is 45 degrees.

To answer this question we will set and solve a system of equations.

Let k be the number of orders that Kala served on Monday, a be the number of orders that Abdul served, and j be the number of orders that Joe served.

Since they served a total of 71 orders, Kala served 5 fewer orders than Abdul, and Joe served 2 times as many orders as Abdul, then we can set the following system of equations:

Substituting the second and third equation in the first one we get:

Adding like terms we get:

Adding 5 to the above equation we get:

Dividing the above equation by 4 we get:

Finally, substituting a=19 in the second and third equation we get:

Answer:

Number of orders Kala served: 14.

Number of orders Abdul served: 38.

Number of orders Joe served: 19.

Segment C prime D prime has endpoints located at C′(0, 0) and D′(4, 0). It was dilated at a scale factor of one half from centre (4, 0). the pre-image

B- segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

According to the question,

Segment C prime D prime has endpoints located at C' (0, 0) and D' (2, 0).

The coordinates are given as:

C' (0, 0) and D' (4, 0).

Since,

Centre of dilation = D = (4,0)

Here, CD seems to be the dilated image of CD by something like a factor of two. It follows that M must have been at (0,0).

It's one-half units left from the centre of dilated.

Then, C` = 1/2 x 4  = 2

Since the dilation is (4, 0),

C = (2+4, 0) = (6,0)

Hence,

segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

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When you capture interaction data in a segment, you can send it (often in real time) to your marketing, product and analytics tools and data warehouses. In most cases, you don't even need to touch the tracking code to connect to the new tools.

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The price of the bookcase in the funiture store is:

$206.72

Given that the markup is 36% of $152

This is:

0.36 * 152 = $54.72

Therefore, the price of the bookcase in the funiture store is:

$152 + $54.72

= $206.72

Recall that the numbers in a die are 1,2,3,4,5,6.

Hence the number of possible outcomes is 6.

We need a number less than 3. Let A be this event.

The favorable outcome is 2.

Since there are 1,2 less than 3 in a die.

Substitute n(A)=2 and n(S)=6, we get

Hence the required probability is 0.333.

Given:

Length(l) of the garden is 3.1 meters

Width(w) of the rectangular garden is 5.6 meters

Area of the garden is 17.36 square meters.

The next step to constructing a tangent line from Q to circle P is to construct the perpendicular bisector of the segment PQ.

For this, Leo can construct arcs from point P and from point Q that are greater than half the length of segment PQ.

The next step is to construct arcs from point P that are greater than half the length of segment PQ.

The domain of the function which is the entire x values during the strike is

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

We use z score formula to calculate :

z = (x-μ)/σ

where,

z = standard score

x = observed value

μ = mean of students height

σ = standard deviation of students height

x  = 63 inches

μ = 70 inches

σ = 3 inches

For x shorter than 63 inches we calculate

Z = (x - μ)/σ

then put the given values in above equation.

= (63 - 70)/3

= -2.33333

Probability value is :

P(x<63) = 0.0098153

Approximately to the nearest thousandth = 0.010

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

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SOLUTION

(a) Complementary angles are angles that add up to 90 degrees. So the angle that will complement 50 degrees will add to it to get 90. Let the angle be x, we have

Hence the measure of the compelement is 40 degrees

(b) Supplementary angles are angles that add up to 180 degrees. So the angle that will supplement 135 degree will add to it to make it 180 degrees. Let this angle be y, so we have

Hence measure of the supplement is 45 degrees

Let x be the number of cups of lemonade sold, and y the number of cups of orange drinks sold, then we can set the following equation:

Now, recall that the standard form of a linear equation is:

Where, A≥0, B and C are integers.

Simplifying the first equation, we get:

Answer:

SOLUTION

Let us make a diagram to interpret the question

from the diagram above, we can make the right-angle triangle as follows

So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.

The adjacent side is d, that is the distance from the seal to the cliff, so we have

Hence the answer is 36 foot to the nearest foot

The solution of the factor with power 2 in the function f(x) can be found as:

(x-2)=0

x=2.

So, the root is x=2.

The multiplicity is the power of the factor (x-2) with its root given as x=2.

So, the multiplicity of the root x=2 is 2.

The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).

Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:

2 · x² + 5 · x - 3 = 0

x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)

x₁₂ = (- 5 ± 7) / 4

x₁ = 1 / 2, x₂ = - 3

Then, the factored form of the inequality is:

(x - 1 / 2) · (x + 3) > 0

In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:

Inequality form - x > 1 / 2 ∨ x < - 3

Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)

The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).

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Question:

Solution:

A quadratic Equation in Standard Form is given by the following formula:

now, the given equation is

this is equivalent to:

According to the Quadratic Equation in Standard Form, we can conclude that

and

GIVEN:

We are told that Jina had an opening balance of $240 in her toll road account.

Also, we are told that the amount left in the toll road account is given by the function;

Required;

(a) To find how much money she has left in her acount after 11 trips.

(b) To find out how many trips she can take until her account is empty.

Step-by-step solution;

We first take note of the variable t, which represent the number of trips taken. Also, the function shows how many trips multiplied by 16 would be subtracted from the opening balance. The result would be how much amount (variable A) would be left in her account.

Therefore;

(a) After 11 trips, Jina would have;

For the (A) part, the answer is $64.

(b) For her account to be empty, then the function given would be equal to zero. That is, after an unknown number of trips, the balance would be zero. We can now re-write the function as follows;

Add 16t to both sides of the equation;

This means after 15 trips she would have emptied her toll road account.

ANSWER: